What do the following two equations represent? $4x-y = -4$ $12x-3y = 1$
Solution: Putting the first equation in $y = mx + b$ form gives: $4x-y = -4$ $-y = -4x-4$ $y = 4x + 4$ Putting the second equation in $y = mx + b$ form gives: $12x-3y = 1$ $-3y = -12x+1$ $y = 4x - \dfrac{1}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.